Design of a Blended Wing Body Aircraft
A project present to The Faculty of the Department of Aerospace Engineering San Jose State University
in partial fulfillment of the requirements for the degree Master of Science in Aerospace Engineering
By
Randhir Brar
December 2014
approved by
Dr. Nikos Mourtos Faculty Advisor ABSTRACT
Blended wing body (BWB) aircraft is more than an idea. NASA in a joint venture with Boeing, has recently completed a highly successful and productive flight test program of experimental
BWB aircraft. These successful flight tests have opened the doors for the further development of
BWB aircraft for potential full-scale commercial aircraft in future. Being very efficient and quiet, the BWB has shown promise for meeting all of NASA's environmental goals for future aircraft designs. This configuration incorporates design features from conventional fuselage as well as traditional flying wing. In this concept, wide airfoil-shaped body is smoothly blended with high lift wings, which means that the entire aircraft contributes to the generation of lift thereby potentially increasing fuel economy and range, while at the same time, massive increase in internal payload is obtained. This report presents the preliminary design of large transport blended wing body aircraft capable of carrying 586 passengers, with range more than 9000 miles. It is also intended for required mission aircraft to meet FAR 25 requirements. 3
ACKNOWLEDGMENT
I would like to thank all people including family members, teachers and friends who supported and motivated me throughout my graduate studies.
First, I would like to express my sincere gratitude to my advisor Dr. Nikos Mortous. His guidance has helped me not only in this project but throughout my graduate program. Without his technical and personal support, this project would not have been possible. He is simple, humble and welcoming to students for any problem. I could not have imagined better advisor to my master program.
Second, I want to acknowledge my brother Manpreet Brar and sister in-law Manbir Brar for their unequivocal support and motivation throughout my studies.
Third, my deepest gratitude goes to my parents, Mohinder Singh and Jeet kaur for their love and care. Throughout the hardships in my life, they always stood by me and helped me. I still remember those sleepless nights my father worked to financially support mine and my brother’s education. And I cannot express enough thanks to my mother with just words. She is simply awesome. All the credit goes to my parents for what I am today.
Above all, I would like to thank my wife Preet Brar for her personal support and great patience at all times. My mere words cannot express kind of support and motivation I got from her. She suffered a lot, worked double shifts to support our living and I can never pay her back for what she did for me. I appreciate her for maintaining patience during phases I was not able to give her time because of my busy study schedule.
Last, but not the least, I would like to thank almighty God. I do not exist without him and
I always believe that whatever he does or happens with me is for my betterment. 4
The Designated Committee Approves the Project Titled
PRELIMINARILY DESIGN OF BLENDED WING BODY PASSENGER AIRCRAFT FOR LONG RANGE
By
RANDHIR BRAR
APPROVED FOR THE DEPARTMENT OF AEROSPACE ENGINEERING SAN JOSE STATE UNIVERSITY
May 2014
Dr. Nikos Mortous Committee Chair, San Jose State University 5 TABLE OF CONTENTS 1.0 Introduction ...... 16 1.1 Motivation ...... 17 1.2 Mission Specifications ...... 18 1.2.1 Range ...... 18 1.2.2 Payload ...... 19 1.2.3 Speed ...... 19 1.2.4 Service Ceiling ...... 19 1.2.5 Climb Rate ...... 19 1.2.6 Takeoff and Landing Distance ...... 20 1.3 Critical Mission Requirements ...... 20 1.4 Sketch of the Mission Profile ...... 21 1.5 Market Analysis ...... 21 1.6 Economic Feasibility ...... 22 1.7 Constraints ...... 23 2.0 Literature ...... 25 2.1 Blended Wing Body Related Concepts ...... 25 2.1.1 Burnelli RB-1 ...... 25 2.1.2 Westland Dreadnought ...... 26 2.1.3 Northrop YB-49 ...... 26 2.1.4 Northrop B-2 Stealth Bomber ...... 27 2.2 Blended Wing Body Prototype Aircraft ...... 27 2.2.1 Boeing X-48 ...... 28 2.2.1.1 X-48A ...... 28 2.2.1.2 X-48B ...... 29 2.2.1.3 X-48C ...... 29 2.3 Comparative Studies of Airplanes with Similar Mission Profile ...... 31 2.4 Three Dimensional Views of Aircraft with Similar Mission Profile ...... 33 3.0 Mission Weight Estimates ...... 35 3.1 Data Base for Takeoff Weights and Empty for Long Haul Transport Jets ...... 35 3.2 Log-log plot for weight data ...... 35 3.3 Comparison of Calculated Regression Coefficient with Roskam Data ...... 36 3.4 Manual Calculation of Mission Weights ...... 36 3.5 Calculation of Mission Weights using the AAA Program ...... 39 6
3.6 Takeoff Weight Sensitivities ...... 39 3.6.1 For the Sensitivity of Take-off Weight to Payload Weight ...... 40 3.6.2 For Sensitivity of Take-off Weight to Empty Weight ...... 40 3.6.3 For Sensitivity of Take-off Weight to Range ...... 41 4.0 Performance Sizing ...... 42 4.1 Summary of Performance Sizing ...... 43 5.0 Center body and Wing design ...... 44 5.1 Airfoil Selection ...... 44 5.1.1 Center Body (Inboard) Airfoil ...... 45 5.1.2 Outboard and Tip Airfoil ...... 46 5.2 Center Body Design ...... 48 5.2.1 Cabin Layout ...... 50 5.3 Wing Design ...... 51 5.3.1 Inboard wing ...... 53 5.3.2 Outboard wing ...... 55 5.3.3 Drawings of wing general layout...... 56 6.0 Selection and Integration of Propulsion System ...... 57 6.1 Propulsion system selection ...... 57 6.2 Disposition of Engines or Integration ...... 59 7.0 Landing Gear Design ...... 60 8.0 Longitudinal Static stability ...... 61 8.1 Basic requirement of longitudinal static stability ...... 61 8.2 Stability for Blended wing body without tail ...... 63 8.2.1 Estimation of neutral point ...... 65 8.2.2 Weight and Balance ...... 66 9.0 Dynamic stability and control ...... 68 9.1 Control surfaces ...... 68 9.2 Longitudinal, Lateral and control derivatives ...... 70 9.3State matrices...... Error! Bookmark not defined. 9.4Control Matrices ...... Error! Bookmark not defined. 9.5 Dynamic Stability Analysis ...... 72 10.0 BWB 601 Drag estimation...... 79 10.1 Calculations of zero drag coefficient for center body (Inner wing) ...... 82 10.2 Calculations of zero drag coefficient for outer wing ...... 83 7
10.3 Calculations of zero drag coefficient for Winglets...... 85 10.4 Calculations of zero drag coefficient for Nacelle...... 86 10.5 Total zero lift coefficient...... 86 10.6 Drag polar...... 87 10.0 Conclusions or Discussions...... 88 8
LIST OF TABLES
Table 1: Routes of BWB 601...... 3 Table 2: Critical mission requirements...... 5 Table 3: Technical specifications of RB-1...... 10 Table 4: Technical specifications of Westland Dreadnought...... 11 Table 5: Technical specifications of Northrop YB-49...... 11 Table 6: Technical specifications of Northrop B-2 Stealth fighter...... 12 Table 7: Technical specifications for X-48A...... 13 Table 8: Technical specifications for X-48 B...... 14 Table 9: Technical specifications for X-48C...... 15 Table 10: Comparison of Long haul passenger airplanes with similar mission profile...... 16 Table 11: Data base for airplanes with similar mission profile...... 20 Table12: Comparison of calculated regression coefficient with Roskam data...... 21 Table 13: Estimated weight fraction for each stage...... 22 Table 14: Weight Sensitivity table...... 26 Table 15: Summary of performance sizing...... 28 Table 16: Comparison of different airfoils for center body...... 30 Table 17: Comparison of different airfoils for outboard and tip...... 31 Table 18: Seat Dimensions...... 36 Table 19: Selected configuration for outboard and inboard wing...... 42 Table 20: Comparisons of some of the world’s powerful jet engines...... 45 Table 21: Point masses and their locations...... 31 Table 22: Dimensionless Aerodynamic stability and control derivatives...... 36 9
LIST OF FIGURES
Figure 1: Mission Profile of BWB 601...... 6 Figure 2: Burnelli RB-1...... 10 Figure 3: Westland Dreadnought...... 11 Figure 4: Northrop YB-49...... 11 Figure 5: Northrop B-2 stealth fighter...... 12 Figure 6: Boeing X-48 A...... 13 Figure 7: Boeing X-48 B...... 14 Figure 8: Boeing X-48C...... 15 Figure 9: 3D Views of 747-400, A380-800 and AN-225...... 18 Figure 10: 3D Views of 747-8I and 747-400...... 19 Figure 11: Log-log plot of your weight data of table 3...... 20 Figure 12: Calculation of Mission Weights using the AAA Program...... 24 Figure 13: Weight design point...... 24 Figure 14: Performance sizing chart...... 27 Figure 15: Airfoil for Center body (NACA 23112)...... 31 Figure 16: Polar plots for NACA 23112 (Reflex) Airfoil...... 31 Figure 17: Airfoil for Outboard and tip Airfoil (FX -60126)...... 32 Figure 18: Polar plots for FX-60126 Airfoil...... 32 Figure 19: Effect of shape on wetted area...... 34 Figure 20: Multi bubble structure...... 35 Figure 21: Integrated skin and shell...... 35 Figure 22: AutoCAD drawing of Cabin Layout...... 36 Figure 23: Effect of thickness ratio and sweep angle on critical Mach number...... 39 Figure 24: Top view of wing (Solid work drawing)...... 44 Figure 25: Front view wing (Solid work drawing)...... 44 Figure 26: Engine type used in relation to speed altitude envelope of airplane...... 45 Figure 27: Genx-2B67...... 46 Figure 28: AutoCAD drawing of Landing Gear layout...... 48 Figure 29: Pitching moment slopes for aircraft A and aircraft B...... 50 Figure 30: Free body diagram of conventional tail wing configuration...... 50 10
Figure 31: Forces acting on swept back wing...... 53 Figure 32: Free body diagram of reflex airfoil...... 54 Figure 33: Cm vs alpha graphs for different CG locations...... 56 Figure 34: Point masses Locations...... 62 Figure 35: CG excursion diagram...... 67 Figure 36: BWB 601 control surfaces...... 68 Figure 37: Time response for unit step input of elevator...... 73 Figure 38: Time response for unit impulse of elevator...... 73 Figure 39: Time response for impulse input of 3 and 4 surfaces...... 78
Figure 40: Time response for impulse input of 5 and 6 surfaces...... 78 Figure 41: Time response for impulse input of 7 and 8 surfaces...... 79 Figure 42: Measurement of projected area of center body and outer wing...... 82 Figure 43: Measurement of wet area of Center body from solid work model...... 83 Figure 44: Measurement of wet area of wing + center body from solid work model...... 84 Figure 45: Measurement of wet area of a winglet from solid work model...... 85 Figure 46: Measurement of wet area of a winglet from solid work model...... 86 11
ABBREVIATIONS
BWB Blended Wing Body GMF Global Market Forecast NASA National Aeronautics and Space Administration NACA National Advisory Committee for Aeronautics NOX Nitrogen oxide FAA Federal Aviation Administration FAR Federal Aviation Regulations MTOW Maximum take-off weight LCD Liquid crystal display MLW Maximum landing weight MZFW Maximum zero fuel weight MCW Maximum cargo volume AR Aspect Ratio SC Service ceiling AAA Advanced Aircraft Analysis CG Center of Gravity AC Aerodynamic Center CAD Computer Aided Design BLI Boundary Layer Ingestion MAC Mean Aerodynamic Chord HP High pressure LP Low pressure SC Service ceiling RC Climb rate 12
NOMENCLATURE
Symbol Definition
WPL Airplane Payload V Airplane Speed R Airplane Range
La Airplane overall length
WTO, W Airplane take-off weight
WE Empty weight
Cj Specific fuel consumption L Lift D Drag
RCR Cruise Range
ELTR Loiter time in hours
WFF Fuel weight fraction of total mission
WF_USED Usable Fuel weight during mission
WRESERVE Weight of reserve fuel
WF Weight of mission fuel
WE-tent Tentative empty weight of airplane
WTO-GUESS Guessed take of weight
WE-allow Allowed empty weight
Mtfo Mass fraction of trapped fuel and oil CR Cruise LTR Loiter
CL Lift coefficient
CLmax Maximum Lift coefficient of airplane (clean)
CLmax-l Maximum Lift coefficient of airplane during landing
Cl-max Maximum Lift coefficient of airfoil
Cmc/4 Pitching moment coefficient at quarter chord
(L/D)max Maximum Lift to Drag Ratio α Angle of attack 13 b Wing span S Wing reference area λ Taper ratio of wing C,
C1 Mean aerodynamic chord
C2 Root chord of inboard wing
S1 Tip chord of inboard wing and root chord outboard wing
S2 Reference area inboard wing b1 Reference area outboard wing b2 Span inboard wing Ʌ Span outboard wing ns Sweep angle
Pm Number of landing gear strut
Pn Maximum static load per strut of main gear
Cm Maximum static load per strut of nose gear 0 Pitching moment coefficient M Rate of change of moment coefficient with respect to α Mcg Pitching moment coefficient at zero angle of attack Mac Pitching Moment h Pitching Moment about CG h0 Pitching Moment about AC Lw Distance of CG from the leading edge of wing ht Distance of AC from leading edge of wing CLw Lift generated by wing Lt Distance of tail AC from leading edge of wing it Wing lift coefficient St Lift generated by tail aw Angle of attack of Horizontal tail Kn Tail reference area Vc Lift Coefficient slope of wing Static margin Vertical component of velocity 14 e Span efficiency ϕ Twist angle of wing Xu Axial force due to velocity Xw Axial force due to incidence Zu Normal force due to velocity Zw Normal force due to downwash lag Zq Normal force due to pitch rate Mu Pitching moment due to velocity Mw Pitching moment due to incidence Mq Pitching moment due to pitch rate Yv Side force due to side slip Yp Side force due to roll rate Yr Side force due to yaw rate Lv Rolling moment due to side slip Lp Rolling moment due to roll rate Lr Rolling moment due to yaw rate Nv Yawing moment due to side slip Np Yawning moment due to roll rate Nr Yawning moment due to yaw rate Xde Axial force due to elevator Yda Side force due to aileron Zde Normal force due to elevator Lda Rolling moment due to aileron Mde Pitching moment due to elevator Ndr Yawning moment due to rudder u Velocity of aircraft along body axis w Velocity of aircraft perpendicular to body axis q Pitch rate Θ Pitch angle ζ Damping ratio ω Un-damped natural frequency 15 v Velocity of aircraft along lateral axis p Roll rate r Yaw rate ϕ Roll angle φ Yaw angle Elevator deflection 16
1.0 Introduction
The conventional aircraft design with fuselage and wing is the most persuasive concept in the aviation industry. This design concept has existed since very first powered flight by wright brothers’ flyer in 1903. Although many design changes have been made throughout the first century of powered flight to improve performance, but even most of today’s aircraft has conventional design; tube and wing as a core. In conventional configuration, both fuselage and wing play separate roles: fuselage carries payload and wings generate lift. The conventional design is well proven and its aerodynamic efficiency has been increased over the period of time.
With more than a century of continuous development, conventional design has reached the stagnation point, leaving very little scope for further improvement in efficiency. The hiking fuel prices and environmental concerns are forcing the aviation industry to look into the new revolutionary concept for high fuel efficiency.
The Blended Wing Body (BWB) configuration is the future of aviation that can offer very high fuel economy along with large payload and quieter & cleaner operation. It is the hybrid shape, with fuselage and wings blended smoothly to make a single lifting surface. The BWB resembles a flying wing, but also incorporates features from conventional aircraft. This combination gives several advantages over conventional tube and wing airframes. As airframe encompasses airfoil shape body blended with the high lift wings, it allows the whole airframe to generate lift that improves the fuel economy. It is expected that BWB aircraft would improve lift to drag ratio by 50 % and fuel efficiency by 20 to 25 % in comparison to conventional configuration [2].
The primary objective of this report is to design a large BWB transport aircraft that has seating capacity of 586 passengers and is capable of achieving transcontinental flights. 17
1.1 Motivation
The first half century of powered flight was mainly concerned about flying longer, faster and higher. In the latter half of century, focus started to shift slowly towards the need of transport with high fuel efficiency, and less noise. In modern world, high efficiency, low noise and cleaner operation became the priority due to increasing fuel prices and environmental concerns. The
BWB is one of the promising alternatives which can meet the demands of the present and future aviation. The BWB configuration offers several advantages over conventional tube and wing configuration [2].
a. Reduction in weight by 10-15 %.
b. Increased fuel efficiency by 20-25 %.
c. Reduction in noise by placing engines on the top of the wings.
d. Increased L/D by 50 %.
e. Reduction in NOX emission BY 17 %.
f. Reduction in operating costs by 10-15%.
g. Large payload volume for the same size of the aircraft.
The primary motivation for this project came from the success of the flight test program of X-48C by NASA and Boeing, which ended in April 2013 [16].This eight-month long flight- test program explored and validated the aerodynamic characteristics of the BWB design concept.
Test results have shown that a BWB aircraft offers a tremendous promise for greater fuel efficiency and reduced noise. It can be controlled as effectively as a conventional tube-and-wing aircraft during takeoffs, landings and other low-speed segments of the flight regime [16].
Also, in recent years, the increased demand of air travel resulted in problems like heavy air traffic, terminal congestion and parking facilities. Large airliner is the demand of time, to carry 18 more passengers while restricting the number of operations from airports. The quest for more people on fewer aircraft has been defined by NASA as “The Lure of Large Aircraft” [2].
Need of high performance, quiet and cleaner aircraft along with the lure of large aircraft is the overall motivation to design large long haul passenger BWB aircraft. In this report, the required mission aircraft is named as BWB 601.
1.2 Mission Specifications
1.2.1 Range
The BWB 601 aircraft is required to fly intercontinentally and must be capable of achieving world longest flights nonstop. BWB 601 will fly the routes listed in table 1.
Range of BWB 601 = Longest route listed in table 1 + Reserve range
Based on required maximum flight distance and reserve range, the range of BWB 600 was decided to be 9800 miles.
Table 1: Routes of BWB 601 From To Distance (miles) Sydney Dallas 8,578 Johannesburg Atlanta 8,439 Dubai Los Angeles 8,339 Dubai Brisbane 8,303 Dubai Houston 8,168 Dubai San Francisco 8,103 19
1.2.2 Payload
Payload includes the weight of passengers, crew, flight attendants and baggage. The mission designed aircraft will carry 586 passengers. A standard number of 3 crew member are required for aircraft operation. The number of the flight attendants depends upon the number of passengers as per FAA regulations. According to FAR section 121.391:
“For airplanes having seating capacity of more than 100 passengers, two flight attendants plus an additional flight attendant for each unit (or part of a unit) of 50 passenger seats above a seating capacity of 100 passengers”.
Therefore for 586 passengers, a minimum of 12 flight attendants are required. For calculation purposes, the standard weight of each person is taken 180 lbs. and baggage 30 lbs. per person. Total payload will be 123060 lbs.
1.2.3 Speed
The maximum speed of subsonic airplane is limited by drag divergence Mach number. At the drag divergence point, drag force on aircraft rises drastically due to transonic effects. It is desired for BWB 601 to fly at maximum possible subsonic cruise speed without entering in drag divergence Mach effects. From the comparison of aircraft with similar mission profile, it was decided that the BWB 601 will fly at a cruise speed of Mach 0.85 and will have a maximum speed of Mach 0.92.
1.2.4 Service Ceiling
The maximum service ceiling of BWB 601 will be 45000 ft.
1.2.5 Climb Rate
The rate of climb will be 4500 ft. /min. 20
1.2.6 Takeoff and Landing Distance
The takeoff and landing distance may seem as performance characteristics of secondary importance, but they are often very crucial from design point of view. It is desirable for the aircraft to meet take-off field length requirements for selected airports with a full payload and fuel. Large passenger aircraft of similar size as that of BWB 601, have takeoff distances at
MTOW in the range of 10,000 ft. and landing distance of 7000 ft. Shortening of these distances, while not a requirement, is a preferred outcome of the BWB 601 model. Specifically, a decrease in takeoff distance as in BWB configuration, offers a high lift to drag ratio.
1.3 Critical Mission Requirements
To be a competitor to similar mission profile airplanes like Airbus 380-800 and Boeing
747 8I, there are some critical mission requirements which must be met. Table 2 lists the critical mission requirements.
Table 2: Critical mission requirements Cruise speed 0.85 Mach
Maximum speed 0.92 Mach
Range 9800 miles
No of passengers 586 21
1.4 Sketch of the Mission Profile
The sketch of mission profile of BWB 601 is shown in a Fig 1.
Cruise@43000 Loiter
Taxi Takeoff Landing Taxi Figure 1: Mission Profile of BWB 601 aircraft
Airbus A380-800 Boeing 747 8I Ann 225 mriya Boeing X-48 1.5 Market Analysis Maximum 89,200 kg 169,100 lb structural (196,700 lb) (76,700 kg) Air traffic is increasing every day due to economic growth, affordability, ease of travel, payload Maximum 184 m3 (6,500 cu ft)[ 5,705 cu ft (162 1,300m3 urbanization and tourism. According to Airbus’ latest Global Market Forecast (GMF), in the next cargo m3) volume two decades (2013 -2032), air traffic will grow at 4.7 percent annually requiring over 29,220 new Cruising Mach 0.89 Mach 0.855 800 km/h (497 mph; speed (945 km/h, (570 mph/917 432 kn) passenger aircraft [22]. According to this rate, the worldwide aircraft fleet will double by 2032. 587 mph) km/h) Maximum Mach 0.96 Mach 0.855 850 km/h (528 mph; Meanwhile, airspace and airport congestion are becoming serious problems in aviation. Saturated speed (at cruise altitude: (570 mph/917 459 kn) at cruise 1020 km/h, km/h; 495 kn) airspace is increasing the probability of disasters due to human errors or malfunctioning of altitude 634 mph Take off run 2,950 m (9,680 ft) communication satellites. The airspace congestion also has been identified as the reason for 60 % atMTOW/SL ISA of delays that the travelers encounter everyday [2]. In order to tackle problems due to the rising Range at 15,700 km 8,000 nmi 15,400 km (9,569 design load (8,500 nmi, (9,210 mi; mi; 8,315 nmi) with airspace congestion, large transport aircraft could be the option to limit the number of increasing 9,755 mi) 14,800 km) maximum fuel; flights. at MTOW with range with 467 passengers maximum payload: and baggage 4,000 km (2,500 mi) According to GMF, in a very large aircraft segment dominated by the A380, there is a Overall 72.73 m (238.6 ft) 250 ft 2 in (76.3 84 m (275 ft 7 in) length m) requirement for 1,334 passenger aircraft in next 20 years. If the market exists for A380 with Height 24.45 m (80.2 63 ft 6 in (19.4Height: 18.1 m (59 ft)[185] m) ft 5 in) conventional tube and wing, then there is definitely a bright market for BWB 601, which offers Outside 7.14 m (23.4 ft) fuselage additional profitability to airliners as discussed in section 1.1. width Outside 8.41 m (27.6 ft) fuselage height Wingspan 79.75 m (261.6 ft)[ 224 ft 7 in (68.5 88.4 m (290 ft 0 in) m) 22
1.6 Economic Feasibility
The BWB airplane is considered to be the next generation airliner. The BWB concept is extremely fuel efficient along with other benefits which includes lower operating costs, lower production costs, reduced airport or airspace congestion, lower fares, reduced environmental impact and improved safety [2]. Fuel efficiency improvement comes from the fact that BWB will have higher lift to drag ratio. Improved efficiency will directly impact the operating cost and ticket fair. Lower production cost is predicted from the fact that BWB body will not involve many tight bends, so manufacturing cost will go down. It is believed that this design concept has more crash survivability than the conventional design [2]. Reduced airport or airspace congestions have already been discussed in previous sections.
Although BWB possesses huge future potential but it should be noted that this concept is still at inception stage. The practical cost related with this project involves costs of research, development, design, testing, safety assessment, certification procedure and maintenance. In order to be commercially successful, mass production of BWB aircraft is required which is a long way journey. But again, as discussed in market analysis section, BWB long haul transport have very good potential market, so can be brought to mass production. Looking at the advantages it can offer, along with reasonable market demands, building such aircraft seems will worth. 23
1.7 Constraints
Some of challenges or constraints faced by BWB configuration are structures and materials, controls, propulsion-airframe integration, systems integration, emergency evacuation and social issues.
Aircraft structure carries aerodynamic loads, weight and cabin pressure loads. The cabin internal pressure loads are carried more efficiently by cylindrical shape (in hoop tension) as in case of conventional aircraft. BWB has non-cylindrical fuselage which makes it hard to carry internal pressure loads and requires heavier structure [4]. There is a need of developing new composite material like graphite stitched epoxy resin, which is stronger enough to carry cabin loads without additional weight [2].
Another important question to ask is- where the windows will be placed in BWB configuration? In this design, there will be only a few passenger windows at the front section and rest of the seats will have multi-functional LCDs for outside views. It is interesting to see how people will get used to such concept. Also according to FAR 25 requirements, passenger aircraft should have that many emergency exits such that it can be evacuated in 90 seconds in case of emergency. In BWB aircraft, fuselage is blended with wings which leave little space on sides of the center body for emergency exits. In order to overcome this issue, emergency exits should be placed on the bottom or top sides of center body.
The lack of conventional tail possesses potential longitudinal and control deficiencies.
Tailless aircraft imposes design challenges to obtain required stability and control. However, by using advanced digital flight controls and envelope limits concepts, such design challenges can be met. 24
BWB configuration also affects the landing approach speed and attitude [29]. The trailing-edge control surfaces flaps cannot be used because the airplane has no tail to trim the resulting pitching moments. Trailing-edge surface deflection is set by trim requirements, rather than maximum lift. This will result in lowering the maximum lift coefficient of a BWB than that of a conventional configuration, and, hence, the wing loading of a BWB will be lower. Also, lack of flap means that the maximum lift coefficient for BWB will occur at a relatively large angle of attack and the flight attitude during approach will be correspondingly high.
Last but not the least, people have been used to the fuselage wing concept for almost ten decades and it will take some time to get them into an unconventional one. 25
2.0 Literature
2.1 Blended Wing Body Related Concepts
Throughout the history, researchers tried to design several aerodynamically efficient concept aircraft such as flying wing and other tailless aircraft. Some of these aircraft related to the blended wing body from history are discussed in this section.
2.1.1 Burnelli RB-1
In 1921, the concept of airfoil shaped fuselage to increase lift was patented by pioneering aviator Vincent Justus Burnelli [6]. Later on, he designed an aircraft named RB-1, which was a twin biplane airliner with lifting body. The body contributed about 27 % of the total lifting area and was designed to support about 15 % of its weight [6]. First flight of RB-1 on 21 June 1921 showed good performance. However, the first model produced was badly damaged while on the ground during a storm.
Table 3: Technical specifications of RB-1 [5][6] Crew [11] 2 Capacity 30 Length 41 ft 2 in Wingspan 74 ft Height 18 ft Empty weight 8137 lb. Gross weight 14637 lb. Figure 2: Burnelli RB-1 [5] 26
2.1.2 Westland Dreadnought
The Westland dreadnought was the experimental aircraft built by Bristol Aeroplane
Company Limited in 1924. This project was aimed to trail the aerodynamic wing and fuselage design of Woyevodsky [25]. This aircraft crashed in its very first flight severely injuring the pilot. Mission was aborted after this incident and no further aircraft was made [25].
Table 4: Technical specifications of Westland Dreadnought [32] Crew 2 Capacity 8 Length 56 ft Wing span 69 ft 3 in Wing area 840 ft2
Figure 3: Westland Dreadnought [32]
2.1.3 Northrop YB-49
The Northrop YB-49 was a purely flying wing jet powered heavy bomber aircraft developed by Northrop Corporation in 1947 [19]. This aircraft had four vertical stabilizers: two on each wing, installed on both sides of the jet engine exhausts. To minimize the flow in span wise direction, the wings were fitted with four air dams extending forward from the vertical stabilizer. Flight testing showed good performance; however, stability issues during simulated bomb runs along with some political issues doomed the flying wing [19]. Although this aircraft was unsuccessful, but it laid the foundation for the development of B-2 stealth fighter.
Table 5: Technical specifications of Northrop YB-49 [19] Crew 7 Length 53.08 ft Height 20.28 ft Wing span 172 ft Wing area 4000 ft2 Figure 4: Northrop YB-49 [19] 27
2.1.4 Northrop B-2 Stealth Bomber
The B-2 spirit, also known as stealth bomber was developed in 1989 by Northrop
Grumman Corporation to have a less exposable cross section to radar [33]. The B-2 design falls between classic flying wing and the BWB concept. It is usually classified as a flying wing, as the protruding body sections are not much larger than the underlying wing shape structure. B-2 is revolutionary from an aeronautics perspective: being efficient can cover long ranges without refueling. It does not have any of the standard stabilizing systems, but flying qualities matches very well with conventional aircraft.
Table 6: Technical specifications of Northrop B-2 Stealth fighter [33] Crew [14] 2 Length 68.56 ft Height 16.73 ft Wing span 170.9 ft
Figure 5: Northrop B-2 stealth fighter [33]
2.2 Blended Wing Body Prototype Aircraft
In 1994, NASA and McDonnell Douglas initiated BWB research under the project named
Advanced Concepts for Aeronautics (ACP) [7]. Under this project, they studied airliner designs of
BWB configuration, which was essentially a flying wing with a wide lifting-body shaped center fuselage. In 1997, a small propeller-driven BWB model airplane of 5.2 m (17 ft) wingspan was built, and test-flown to demonstrate the flying characteristics [7]. The ACP studies ended in 1998 with revolutionary conclusions such as increase in L/D drag ratio, reduction in take-off gross weight and reduction in operating costs [7]. NASA and Boeing continued their BWB research and 28 in early 2000, Boeing began the construction of the BWB-LSV- an unmanned, 14% scale vehicle of the BWB transport, to evaluate the design in actual flight tests [23]. Later on in 2001, this project was named as X-48.
2.2.1 Boeing X-48
The Boeing X-48 is a BWB, experimental unmanned aerial vehicle, developed by NASA and Boeing to investigate feasibility of large BWB airliner. During the last decade, various X-48 models have been developed, followed by a series of ground and flight tests. According to
NASA, X-48 design holds a very good promise of efficient large passenger aircraft. The variants of the X-48 investigated by NASA are discussed in following sections.
2.2.1.1 X-48A
The X-48A was primarily made of composites, had a wing span of 10.7 m and was powered by three small Williams J24-8 turbojets [23]. This was the small scaled model project which started in 2001 and it was expected to complete ground tests in 2003 [23]. However, the project was cancelled in 2002 due to some technical problems in the flight control system along with changing priorities of NASA.
Table 7: Technical specifications for X-48 A [23] Length ? Wingspan 10.7 m (35 ft) Weight 1130 kg (2500 lb.) Speed 265 km/h (165 mph) Ceiling ? Propulsion 3x240 lb. Williams J24- 8 turbojet Figure 6: Boeing X-48 A [23] 29
2.2.1.2 X-48B
After the cancellation of the X-48A in 2002, Boeing contracted Cranfield Aerospace (UK) to design and build a smaller BWB model [23]. In 2005, this BWB was designated as X-48B. The X-
48B was remotely controlled aircraft, built to 8.5 % scale model of potentially flying aircraft
[23]. Extensive ground tests were conducted in 2006, to validate engine, fuel system, battery endurance, the telemetry link, the flight-control software, and the aircraft's taxing characteristics
[23]. Phase I flight tests were conducted at NASA's Dryden Flight Research Center in early 2007 to determine low speed, low altitude characteristics including engine out, stall and handling characteristics [18]. Phase II high speed flight tests took place in spring 2008 on modified X-
48B. By April 2009, fifty X-48B flights had been completed successfully [23]. Flight tests demonstrated that BWB can aircraft can be flown as safely as current transport having traditional fuselage, wings and tail configuration.
Table 8: Technical specifications for X-48 B [23] [4] Length ? Wingspan 6.22 m (20 ft 5 in) Weight 225 kg (500 lb.) Speed 220 km/h (120 knots) Ceiling 3000 m (10000 ft) Propulsion 3x Jet Cat P200 turbojet
Figure 7: Boeing X-48 B [18]
2.2.1.3 X-48C
The X-48C was updated version of the X-48B, with some modifications, to reduce the noise level and for better stability controls [18]. Modifications included reducing the number of engines to two, and adding two vertical fins to shield the engine noise. Three 50-pound thrust jet engines of X-48B's were replaced with two 89-pound thrust engines [18]. Also, it was equipped 30 with modified flight control system software which included flight control limiters to keep the aircraft flying within the safe flight envelope. The X-48 C retained most dimensions of B model.
The aft deck of the aircraft was extended about two feet to the rear and wing span increased by one inch. The X-48C was aimed to evaluate the low-speed stability and control of a low-noise version of a BWB aircraft. This aircraft made its first successful flight on Aug. 7, 2012 at
Edwards Air Force Base [18].
The success of X-48 mission has proved that BWB configuration offers significantly greater fuel efficiency and reduced noise, can be controlled as effectively as a conventional tube-and-wing aircraft during takeoffs, landings and other low-speed segments of the flight regime [18].
Table 9: Technical specifications for X-48 C [23] [18] Length ?
Wingspan 6.25 m (20 ft 6 in)
Weight 225 kg (500 lb.)
Speed 220 km/h (120 knots)
Ceiling 3000 m (10000 ft)
Figure 8: Boeing X-48C [18] Propulsion 2x SPT15 Jet Cat Ducted Fan 31
2.3 Comparative Studies of Airplanes with Similar Mission Profile
Table 10 shows the tabulated comparisons of similar mission profile aircraft. Antonov
AN- 225 Mriya is the world largest commercial aircraft in-operation [9]. The AN-225, is powered by six engines, three per wing and has two tails. Dimensions of AN-225 are mind blowing with fuselage of 275 ft and wing span of 290 ft [9]. Also, maximum takeoff weight is an unbelievable
1,323,000 pounds. Ann 225 is cargo aircraft while the other three listed in table are passenger airliners.
Boeing 747-8I is slightly longer than the Airbus A380-800, with 250 ft 2 inch length compared to 245 ft length of the A380-800. However, the A380-800 is taller, has a larger wingspan and more maximum takeoff weight compared to B747-8I. Also A380-800 has the largest passenger capacity in the world. The boing 747-400 is little smaller in length however it is best-selling airplane in 747 series. For more detailed comparison, see table 10.
Table 10: Comparison of Long haul passenger airplanes with similar mission profile [17][9] A380-800 747-400 747 8I Ann 225
Crew 2 2 2 6
Seating capacity 855(Maximum) 660 (Maximum) 605(maximum) N/A 525-555 (3-class) 416 (3-class) 467 (3-class) MTOW (lbs.) 1,268,000 910,000 987,000 1,410,958
MLW (lbs.) 869,000 688,000
MZFW (lbs.) 814,000 651,000
3 MCV (ft ) 6,500 5,705 45909 Cruising speed Mach 0.89 Mach 0.855 Mach 0.855 Mach 0.653
Maximum speed Mach 0.96 Mach 0.92 Mach 0.855 Mach 0.694
Take-off 9,680 10,200 distance (ft) 32
Range (miles) 9,755 8826 9,210 9,569
Overall length 245-0 231-10 250-2 275-7 (ft-inch) Height (ft-inch) 80-0 63-8 63-6 59-5
Outside width 23-5 (ft-inch) Outside fuselage 27-7 height (ft-inch) Wingspan 261-7 211-5 224-7 290 (ft-inch) 2 Wing area (ft ) 9,100 6027.78 9,740 Aspect ratio 7.5 7.4 8.6
Service ceiling 43,097 43,000 43,000 36,089 (ft) Engines 4xTrent 900 4xPW 4062 4xGEnx-2B67 6 × ZMKB 4xGE CF6- 80C2BF5 Thrust 75,000 lbf 4x63,300 lbf 4x66,500 lbf 51,600 lbf 4x62100 lbf 33
2.4 Three Dimensional Views of Aircraft with Similar Mission Profile
Figure 9: 3D Views of 747-400, A380-800 and AN-225 [9] 34
Figure 10: 3 D Views of 747-8I and 747-400 [31] 35
3.0 Mission Weight Estimates
3.1 Data Base for Takeoff Weights and Empty for Long Haul Transport Jets
Table 11: Data base for airplanes with similar mission profile [17] [9][31] Aircraft WTO (lbs.) WE (lbs.) Log10 (WTO) Log10 (WE) Boeing 747-400 ER 910,000 406,000 5.959041392 5.608526034 747-400 875,000 394,088 5.942008053 5.595593211 747-100 735,000 385,000 5.866287339 5.58546073 747-200 833,000 383,000 5.920645001 5.583198774 747-300 833,000 392,800 5.920645001 5.594171479 767-400 ER 450,000 229,000 5.653212514 5.359835482 777-200 LR 766,000 326,000 5.88422877 5.5132176 777-300 660,000 353,000 5.819543936 5.547774705 777-300 ER 775,000 366,940 5.889301703 5.564595057 787-9 540,000 254,000 5.73239376 5.404833717 Airbus A 380-800 1,235000 608,400 6.091666958 5.784189205 A 340-600 811,300 392,000 5.909181476 5.593286067 A 340-500 820,100 376,800 5.913866812 5.576110894 A 340-300 606,000 285,000 5.782472624 5.45484486 A 330-300 507,000 267,200 5.705007959 5.426836454
3.2 Log-log plot for weight data
Figure 11: Log-log plot for weight data 36
3.3 Comparison of Calculated Regression Coefficient with Roskam Data
The estimated values of regression coefficient by Roskam and calculated values are shown in table 12. Calculated values are very close to Roskam data. Therefore, for further calculations, calculated value of regression coefficients will be used.
Table 12: Comparison of calculated regression coefficient with Roskam data Regression Coefficient Calculated Value Value according to Roskam A 0.0795 0.0833 B 1.0433 1.0383
3.4 Manual Calculation of Mission Weights
For initial estimation of weights, reference [24] is used. There is no practical data available for
BWB configuration and method used in Reference [24] is for conventional airplane, therefore, some additional assumptions are made to get best initial estimation.
Assumptions:
(A). For cruise lift to drag ratio ( ) = 25
(B). For loiter ( ) = 24.5
These assumptions are made on the basis of reference [2], which claims that L/D ratio of BWB is
50% higher than conventional configuration.
Procedure for estimating weights:
Step 1. The mission payload weight was assumed as 126000 lbs. 37
Step 2. For initial guessing of mission TOW benchmarking was done with Boeing 747 8I and it was assumed the blended body would result in 20% weight saving. Therefore WTO-Guess = 789600 lbs.
Step 3. It consists of calculating mission fuel weight. For this, weight fraction of each stage of mission profile is estimated and then all fractions are multiplied to get total fuel fraction of mission. Mission profile stages and their estimated fuel fractions are listed in table 13.
Table 13: Estimated fuel fraction for each stage
Stage name Begin weight Weight Equation used or Reference and end weight fraction Stage 1 -Engine start WTO ,W1 W1/WTO=0. 990 Reference[24] and warm up Stage 2- Taxi W1 ,W2 W2/W1=0.990 Reference[24]
Stage 3- Take-off W2 , W3 W3/W2=0.995 Reference[24]
Stage 4- Climb to W3 , W4 W4/W3=0.90 Reference[24] cruise altitude and accelerate to cruise speed
Stage 5 - Cruise W4 ,W5 W5/W4=0.741 4 = ( ) ( ) (1)
5
Where, = 0.5 /( /
ℎ ) , RCR= 9712 miles,
Assumption ( ) = 25
Stage 6- Loiter W5 , W6 W6/W5=0.992 1 5 = ( ) ( )
6 (2)
= 0.6
Assumption ( ) = 24.5
and ELTR= 0.33 hrs. Stage 7 - Descent W6 ,W7 W7/W6=0.990 Reference[24]
Stage 8 - Flying to W7 ,W8 W8/W7=0.990 Reference[24] the alternate airport. 38
Stage 9 - Landing, W8 ,W9 W9/W8=0.992 Reference[24] taxi and shut down
Total mission used fuel fraction WFF is given by:
1 2 3 4 5 6 7 8 9 WFF=( ) ( ) ( )( )( ) ( ) ( )( ) ( )=0.634 (3)
1 2 3 4 5 6 7 8
_= (1 − ) = 289783.2 lbs.
Weight of mission fuel (WF) = weight of fuel used +weight of trapped fuel
WF= 292625.76 lbs.
Step 4. WE-tent = WTO-guess - WF - WPL (4)
WE-tent = 789600 – 292625.7- 123060 = 372369 lbs.
Step 6. To find WE-allow, the following equation was used:
WE-allow = invlog10 [(log10 WTO -- A) / B] (5)
Where the regression coefficients A and B were found to be 0.0795 and 1.0433.
WE-allow= 377091 lbs.
Step 7. The WE-tent and WE-allow are not within the 0.5% tolerance, therefore further iterations are needed. After iterations, Final weight: WTO= 823767 lbs., WE= 392718 lbs. 39
3.5 Calculation of Mission Weights using the AAA Program
Figure 12: Calculation of Mission Weights using the AAA Program
Figure 13: Weight design point
3.6 Takeoff Weight Sensitivities
It is important to conduct weight sensitivities analysis in order to find which parameters drive the design and which areas of technological change to be pursued in case new mission capability must be achieved. For takeoff weight sensitivities, calculations reference [24] is used. 40
3.6.1 For the Sensitivity of Take-off Weight to Payload Weight
= ( − (1 − ) )−1 (6)
Where, A and B were calculated in section. C and D are calculated using the following equation
= {1 − (1 −)(1 − ) −) (7)
= (8)
Here, Mtfo can be assumed to be zero and Mres=.10, from the calculations, C=0.670 and D= 123060 = 5.83
The factor 5.83 is the growth factor due to payload for BWB 600 aircraft. This means that for each pound increase in payload weight, the gross take-off weight will have to be increased by
5.83 lbs.
3.6.2 For Sensitivity of Take-off Weight to Empty Weight
= [ { 10− }]−1 (9)
10
= 2.19
The factor 2.19 is the growth factor due to empty weight for BWB 600 aircraft. This means that for each pound increase in empty weight, the gross take-off weight will have to be increased by 2.19 lbs. 41
3.6.3 For Sensitivity of Take-off Weight to Range
−1
= { } (10)
F = −BW 2{CW (1 − B) − D}−1(1 + M )M (11) res f TO TO F=3361834.85 lbs. = 124.5 /
The factor 124.5 is the growth factor per unit range for BWB 600 aircraft. This means that for each mile increase in range, the gross take-off weight will have to be increased by 124.5 lbs.
Table 14: Weight sensitivity table
∂WTO 5.83
∂WPL
∂W TO 2.19
∂WE
∂WTO 124.5 lbs/miles
∂R 42
4.0 Performance Sizing
The aircraft is sized according to FAR 25 requirements. The design point is obtained from the performance graph plotted according to reference [24].
Figure 14: Performance sizing chart 43
4.1 Summary of Performance Sizing
The design point chosen is shown as point P on the sizing graph. The table shows the initial specifications of BWB 601 according to design point.
Table 15: Summary of performance sizing 2 Take-off wing loading (lbs./ft ) 92
Aspect ratio 6
Stall speed (knots) 140
Wetted area (ft2) 31471
2 Wing area (ft ) 9601
Take-off thrust (lbf) 264,990
Maximum take-of lift coefficient required 1.6 with flaps up (clean) CLmax Maximum lift coefficient required for landing 2 CLmax-l 44
5.0 Center body and Wing design
5.1 Airfoil Selection
The selection of airfoil is very important aspect of design. While high lift and low drag coefficients are the requirements of performance, the moment coefficient (Cm) plays a role in stability behavior of an airplane: it affects the longitudinal stability. In conventional airplane, airfoil is designed for negative moment coefficient, which is compensated by the horizontal tail to stabilize longitudinally. Tailless aircraft obviously can't compensate for negative moment as they don’t have horizontal tail. Longitudinal stability of tailless aircraft can be obtained in two ways: using reflex airfoil or by using Sweep and twist wings [12]. How these two designs incorporate stability will be discussed in detail in stability section of this report.
In case of swept back wing, any airfoil can be used by selecting a suitable combination of sweep and twist [12]. Longitudinal stability is provided by combination of sweep and twist. In order to get good performance, it is best to choose airfoil with very low pitching moments. The low pitching moment airfoil thus will require smaller amount of twist which results in a broader speed range without paying too much penalties off the design point.
Both, increasing reflex in camber line and twist in swept wing affect the performance, so it is desired to select airfoil which is best suited for required mission. Keeping performance in mind, it was decided to use reflex airfoil for center body and cambered airfoil for outboard and tip. Stability for airplane will be achieved through combination of center body airfoil (reflex) and wing twists, whereas high lift and ‘high lift to drag ratio’ will be achieved from outboard cambered airfoil. 45
5.1.1 Center Body (Inboard) Airfoil
The airfoil chosen for center body should have medium thickness, large leading edge radius, high stall angle, possible high lift to drag ratio along with positive pitching moment coefficient. Java foil software, which is interactive database and program, was used to analyze different airfoils listed in table 15. The present conceptual design work selected NACA 23112
(Reflex) as the most suitable for the center body of BWB601. Shape and Polar plots for NACA
23112 generated by using ‘Java foil’ are shown in Fig 15 and Fig 16.
Table 16: Comparison of different airfoils for center body Lie back NACA Eppler MH-62 MH-60 LA2573 A 23112 635 Max Camber 3.2% at 1.2% at 2.889 1.5% at 1.8% at 26.1% C 14.7% C 37.4% C 38.10%C Max Thickness 13.7% 12% 11.616 9.30% 10.28%
Cl-max 1.3 1.55 0.964 1.2 0.906
Cm-c/4 0.02 0.03 .04 -0.004 +0.0175
(L/D)max 18.549 42.28 22.883 67.897 65.726
Stall angle 12 13 14 8.0 9.0
Angle of attack 10.5 4.5 4 6.5 6.0 for Max L/D Zero lift angle 0.0 -0.5 0.5 -0.5 0.0
Lower flatness 56.1 72.1 % 64.6% 68.3% 65.0%
Leading edge 3.2 3.8 % 2.1 % 0.6 % 0.6 radius Trailing edge 7.0 14.40 13.4 4.3 4.6 angle 46
Figure 15: Airfoil for Center body (NACA 23112)
Figure 16: Polar plots for NACA 23112 (Reflex) Airfoil.
5.1.2 Outboard and Tip Airfoil
The outboard airfoil is crucial part of aircraft design as majority of the lift will be generated by this section. Also, the region in between outboard and Tip will be holding fuel and main landing gear, therefore it must be of considerable thickness. So, outboard and tip airfoil should have high lift to drag ratio, high lift, high thickness and good stall characteristics. Number of candidate airfoils (as listed in table 17) were studied and compared to select the best airfoil. From the comparison the FX
60-126 airfoil was selected for outboard and tip sections of wing. Shape and Polar plots of FX 60-
126 airfoil generated by using ‘Java foil’ are shown in Fig 17 and Fig 18.
Table 17: Comparison of different airfoils for outboard and tip FX60-126 GOE 440 Eppler 395 FX 61-140 MH 115
Max Camber 3.6% 9.7% 5.3 2.5% 5.6% 47
Max Thickness 12.6% 15.2% 12.3 14% 11.1
Clmax 1.491 1.864 1.589 1.422 1.725
(L/D)max 145.5 117.308 106.8 105.93 107.008
Stall angle 10 0.50 8.0 6.5 7.0
Angle of attack for 5 2.50 5 5.5 4.5 Max L/D Zero lift angle -4.5 -11.50 -6.5 -5.0 -6.5
Lower flatness 52.8% 74.8% 69.9 27.8 84.7%
Leading edge 2.6 3.2% 0.8 1.2% 1.6 radius Trailing edge angle 2.6 9.5 7.4 6.3 7.2
Figure 17: Airfoil for Outboard and tip Airfoil (FX -60126)
Figure 18: Polar plots for FX-60126 Airfoil. 48
5.2 Center Body Design
In Blended Wing Body configuration, both the fuselage (center body) and wings are integrated with each other smoothly and acts as a single body. The center body is composed of distinct and separate wing structures, though the wings are smoothly blended into it.
The center body or fuselage results in most of the drag of the airplane (25-50 percent), therefore center body of aircraft is designed in a shape to have minimum possible drag. Various drags which act on fuselage are [6]:
(A). Friction drag
(B). Profile drag
(C). Base drag
(D). Compressibility drag or wave drag
(E). Induced drag
In order to have minimum friction drag, minimum wetted area is required for a given volume, which further depends upon the shape of the body. Effect of shape on wetted area can be observed in
Fig 19. Sphere is the best option for minimum friction drag but it’s not conducive to the streamlines and thus increases drag. Flatted disc is the second best option for minimum friction drag [14]. Profile and base drag is determined by the front and after body shape. To have minimum profile and base drag, ideal streamline flow is required over nose and tail. The drag related with compressibility due to high speed is called compressibility drag. The compressibility drag includes any variation of the viscous and vortex drag with Mach number, shock-wave drag, and any drag due to shock-induced separations. Compressibility drag can be reduced by increasing sweep angle. 49
Cylinder shape used in conventional airplanes has lesser frontal area that results in lesser profile and base drag as compared to BWB configuration. But cylindrical fuselage has more frictional drag due to more wetted area than BWB fuselage for same volume
During designing of fuselage, trade-off has to be made between various drags to get best possible shape. For BWB 601 fuselage, sphere is flattened to streamlined disk, which is integrated with wings to have minimum wetted area.
Figure 19: Effect of shape on wetted area [14]
The cabin has to be designed for internal pressure in addition to bending, shear and torsional loads. It should be noted that disc shape cabin requires more strength for same internal pressure as compared to conventional cylindrical; this is due to the fact that in a conventional cylindrical fuselage, internal pressures are carried more efficiently in hoop stresses by a thin skin, whereas for disc shape fuselage, internal pressure induces large bending stresses which require heavier structure.
Studies have been conducted by NASA and Boeing to address this structural issue [4]. They investigated two concepts: Multi bubble fuselage structure and single strong shell (Fig 20 and Fig
21). Multi bubble structure consisted of cylindrical shells inside main disc for sustain internal pressure loads and outer skin to support bending. Boeing argued with multi-bubble theory and raised the issue that outer skin still needs to be designed to take internal pressure loads in case there is any leakage in the inner bubble. As the outer skin has to be designed for internal 50 pressure, there is no point to build inner shells. Their research concluded to use single shell structure strong enough able to withstands all the loads. The additional weight due to heavy structure should not be problem as the aerodynamic gains from BWB configuration will outnumber this weight increase. For BWB 601 cabin design, single shell approach will be used (Fig 21).
Figure 20: Multi bubble structure [4] Figure 21: Integrated skin and shell [4]
Overall structural configuration of BWB will be swept back wing body. A swept back wing offers the advantage of delaying drag rise caused by compressibility near sonic speeds, so they are favored for high subsonic and supersonic speeds. Center body has the maximum thickness that will cause high drag, therefore needs higher sweep than outboard wing.
5.2.1 Cabin Layout
For passenger aircraft, design of cabin layout must meet FAR 25 requirements. The fuselage of BWB 601 is required to enclose a space for total number of 601 people (including flight attendants) plus galleries, lavatories and space for baggage. Size of cross section is mainly affected by number of seats abreast. Higher abreast seating capacity provides the opportunity for extension in coming models and thus shorter the fuselage, easier it becomes to grow plane in future. The BWB body gives the advantage of higher abreast seating. Cabin layout is designed according 51 to reference [24]. The cabin is designed for 28 First class, 86 business class and 472 economy class seats. The dimensions of seats for these three categories are listed below in table 18. Space for 18 galleries and 25 lavatories is provided considering the large number of passengers.
Table 18: Seat Dimensions Seat Width Seat Pitch Aisle Width
First class 25 40 23
Business class 23 36 21
Economy class 21 32 20
Figure 22: AutoCAD drawing of Cabin Layout
5.3 Wing Design
This section deals with some of the considerations involved in wing design, including the selection of basic sizing parameters and more detailed design. Wing is the most important aspect of aircraft design, which decides how well the airplane will fly. Wing design or shape depends upon the mission requirements: type of aircraft, performance, speed, operating altitudes, gross weight, and space requirements for engine and fuel tanks. Depending upon mission requirements, wing configuration can be selected from following: 52
a) Rectangular configuration
b) Elliptical configuration
c) Swept wing configuration
d) Delta wings configuration
While each configuration works well, they all have certain restrictions and limitations making them suitable only for certain requirements. The swept wing is the “way to go” for jet powered aircraft. It needs more forward speed to produce lift than the rectangular wing, but results in much less drag in the process, meaning that the aircraft can fly fast with higher efficiency. It also works well at the higher altitudes, which is where most jet aircraft fly [20].
There are essentially two approaches to wing design [34]. In the direct approach, one finds the planform and twist that minimize some combination of structural weight, drag, and CL- max constraints. The indirect approach involves selecting a desirable lift distribution and then computing the twist, taper, and thickness distributions that are required to achieve this distribution. The latter approach is generally used in preliminary design to obtain analytic solutions and insight into the important aspects of the design problem, but is difficult to incorporate certain constraints and off-design considerations in this approach. The direct method, often used in the latter stages of wing design for depth investigation on preliminary selected parameters. In this report, indirect approach is used to design a wing.
Wing lift and load distributions play a key role in wing design. Main objective of wing design is to generate the lift such that the span wise lift distribution is elliptical [34]. Elliptical lift distribution ensures lower induced drag, lighter wing structure, better control and stall characteristics. From performance sizing section, wing surface area and aspect ratio were calculated as 9601 ft2 and 6 respectively. Wing span can be calculated from equation 53
2 = → b= 240 ft (12)
In blended body case, the wing and fuselage (center body) act as single lifting surface.
The center body is referred to as inboard wing and the outer body is referred to as outboard wing in this report. Both Inboard and outboard wing parameters are driven by different requirements and must met their individual needs. Inboard need to be thicker than outer one to meet the volume requirements of cabin.
5.3.1 Inboard wing
Inboard wing design is designed to carry payload load as well to generate lift. Most of the dimensions are decided by the cabin volume requirement. Wing thickness ratio is decided by airfoil used, = 12 from center body airfoil selection. For BWB, the center body frontal area is large so high drag is expected unless high sweep is provided to wing. Also high thickness ratio would result in low critical Mach number i.e. early rise of drag. To increase the critical Mach number, design requires high wing sweep. Figure 23, depicts the effect of thickness ratio and sweep angle on critical Mach number. For initial design, sweep angle 60 degree is chosen to avoid early rise of drag.
Figure 23: Effect of thickness ratio and sweep angle on critical Mach number [24] 54
Taper ratio is calculated as 36.1 1 = 1 = = 0.306 2 117.8
Calculations of inboard wing characteristics and parameters: (13)
2 (A). Inboard wing area S1= Area under Fig 22= 4813 ft
(B). From airfoil (NACA 23112) characteristics Cl-max =1.555
−0.4 = (C). − [24] ∞ (14)
Where, W take-off weight of airplane in newton, WF is mission fuel weight, q∞ is
free stream dynamic pressure at 43000 ft.
1 2 = ρ (15)
∞ 2 ∞
ρ = 0.262 kg/m3
= .319 Using equations (14) and (15), we get −
(D). = [37] (16)
−
∞ 2
= −1 ( ) (17)
Where, Vc is the vertical components of velocity during climb.
From equations (16) and (17), we get − = 0.807 (E) To figure out the twist Stanford Java Wing analysis program is used [27]. This program uses discrete vortex Weissinger computations to calculate and plot the lift & coefficient of lift distributions, and also displays efficiency & induced drag coefficients. Twist angle was varied to get lift distribution close to elliptical distribution (e=1). From this trade study twist angle ( 1) = 0 degree. 55
5.3.2 Outboard wing
Calculations of outboard wing characteristics and parameters:
2 (A). Outboard wing area, S2=S-S1= 4798 ft .
(B). Wing span for outboard wing b2= b-b1= 240-76= 164 ft. 2
2 = 2 = 5.6 Aspect ratio for outboard wing can be calculated as 2
(C). Using equations (14) and (15), we get − = .320
(D).
(E). Using equations (16) and (17), we get − = 0.809
(F) From airfoil (FX -60126), Cl-max=1.499
Again, Stanford Java Wing analysis program is used [27] to find out twist in wing. Sweep angle and twist angle were varied to get lift distribution close to elliptical distribution (e=1). From this trade study twist angle ( 1) = 4 degree.
Table 19: Selected configuration for outboard and inboard wing CLmax Stall Taper ( ) Sweep Twist e Dihedral angle angle Λ angle ϕ angle (degree) (degree) Outboard 1.44 18.5 0.5 30 4 0.995 3 wing Inboard 1.27 27.5 0.302 60 0 0.987 0 wing 56
5.3.3 Drawings of wing general layout.
All dimensions in inches.
Figure 24: Top view of wing (Solid work drawing)
Figure 25: Front view wing (Solid work drawing) 57
6.0 Selection and Integration of Propulsion System
6.1 Propulsion system selection
Type of propulsion system used in an airplane depends upon the mission requirements and other factors like cost, reliability, maintainability and timely certification. Turbofan type engine was selected after comparing the mission profile of BWB 601 with Fig 32 [24].
In order to avoid complexity of development and certification of engine, it was decided to select engine that is already existent in market. Trade study was done between the different engines listed in table 20 to pick engine for BWM 601.
Figure 26: Engine type used in relation to speed altitude envelope of airplane [6]
Table 20: Comparison of some of the world’s powerful jet engines [8] [10] GEnx-2B67 GEnx-1B70 Trent 900 GE 90-115 B (B747-8) (B787) Takeoff thrust (lbs) 67000 69800 75,000–84,000 115000
Bypass ratio 8.0 9.1 8.5-8.7
Overall pressure ratio 44.7 43.5 37-39 42
Air Mass flow 2297 2545 (lbs./sec) 58
Fan Diameter 104.7 111.1 155.3 126.7 (inch) Bare engine length 169.7 184.7 215 287 (inch) Compressor stages 1/3/10 1/4/10 1/8/6 1/4/9 (Fan/booster/HPC) Turbine stages 2/6 2/7 1/5 2/6 (HP/LP) Thrust to weight ratio 5.64 5.46-6.11 6.3
Dry weight (lbs.) 12400 12822 13770 18260
Out of the engines listed in table 20, Genx-2B67 and Trent 900 are well proven engines for large transport aircraft and they are being used in Boeing 747-8I and Airbus A380 respectively. Although both these engines are very efficient and reliable, but for the required mission, aircraft Genx-2B67 has more to offer than Rolls Royce’s Trent 900. Genx-2B67 is smaller in size and is lighter in weight compared to Trent 900, which gives advantages like less drag and more aerodynamic efficiency. The Genx-2B67 produced by GE aviation uses latest generation materials and design processes to reduce weight, improve performance and requires less maintenance [30]. BWB 601 requires 264,990 lbf of takeoff thrust; therefore, four Genx-
2B67 (4x67000) engines will be used. The selected engine meets all the mission requirements along with low fuel burn and excellent environmental attributes.
Figure 27: Genx-2B67 [11]. 59
6.2 Disposition of Engines or Integration
The engine will be placed on the top of center body at aft location, to offer noise shielding. There are two options for aft engine mounting: First one is, simply mounting the engines on pylons, but for this, penalty of increased wetted area, weight and ram drag has to be paid. Second option is to mount engine directly on the upper surface and take the advantage of ingestion of the boundary layer generated. In principle, boundary layer ingestion can improve the propulsive efficiency by reducing ram drag. This assumes that an inlet can be designed such that it provides proper pressure recovery and uniform flow at the fan face of the engine.
Studies on the boundary layer ingestion concept were conducted at the University of
Southern California and at Stanford University [29]. Results showed that proper configurations of vortex generators could provide a reasonably uniform flow at the fan face with acceptable pressure recovery. Although boundary layer concept requires further investigation to validate it for practical application, but in this report, it is assumed that results will hold good for practical aircraft. Therefore, three-engine configuration with upper surface boundary layer ingestion inlets and S-ducts to the engines is selected. 60
7.0 Landing Gear Design
A retractable two twin tri-tandem main landing gear is chosen to provide enough strength required during landing and take-off of large passenger aircraft. The design of landing gear depends on tip over criteria and ground clearance criteria [24]. To provide adequate ground clearance, the length of nose gear is chosen as 11 ft and for middle & rear tandem landing gear as
10 ft.
The nose gear is located at 10 ft, center tandem at 68.3 ft and rear tandem at 95 ft from nose respectively. The maximum static load per strut for main gear (Pm) and nose gear (Pn) can be calculated from following equations as [24]:
= 0.94 (22)
= 0.06 (23)
Where, WTO is gross takeoff weight and n=4 is the number of main gear struts. By using equation
(22), (23) and typical landing gear data [24], other specifications can be easily obtained.
AutoCAD drawing of general layout is shown in Fig 34.
Figure 28: AutoCAD drawing of Landing Gear layout 61
8.0 Longitudinal Static stability
8.1 Basic requirement of longitudinal static stability
Static stability describes the aircraft’s initial response to a disturbance. If the aircraft has tendency to return back to equilibrium after a disturbance, then it is called positive static stable and if it continues in perturbed state, then it is called neutrally stable and if it moves further away from equilibrium state, then it is called negative static stable aircraft.
Longitudinal stability means ability of aircraft to recover from an angle of attack disturbance. This quality of aircraft is also called pitch stiffness and is defined as change in pitching moment coefficient for a given change in angle of attack. For the aircraft to be statically stable in pitch, the variation in pitching moment with alpha must be negative. Therefore an increase in angle of attack will generate a negative pitching moment about the CG, bringing the aircraft back to its trim condition. Therefore, for aircraft to be stable, < 0.
Now consider two airplanes A and B as shown in the Fig 35. Both aircraft have positive static stability i.e. < 0.The slope line of aircraft A intersects the x axis at positive angle of attack whereas slope line of aircraft B intersects x axis at negative angle of attack. This means that aircraft A can be trimmed at positive angle of attack whereas aircraft B cannot be trimmed at positive angle of attack. In other words, in order to trim aircraft at positive angle of attack, it is required to have 0 > 0. To sum up, following two conditions must be met for positive pitch stability:
< 0 (24)
0 > 0 (25) 62
Figure 29: Moment slope of aircraft A and aircraft B
Consider wing and tail configuration as shown in Fig 36. For this analysis, the moments generated by fuselage, propulsion system and drag on tail have been neglected. It is also assumed that angle of attack is small such that cos α=1
Figure 30: Free body diagram of conventional tail wing configuration [10]
=+ (ℎ − ℎ ) − (ℎ − ℎ) 0 (26) Non- dimensionalzing the above equation by dividing with ,
= + (ℎ − ℎ ) − (ℎ − ℎ) (27)
0
Assuming linear varition of tail lift coefficent , can be defined as
= [ (1 − ℇ⁄ ) − ] (28) 63
Also wing lift coefficient can be expressed as linear relationship, = Therefore, ℇ = + (ℎ − ℎ0) − (ℎ − ℎ) [ (1 − ⁄ ) − ]
For α=0,
= + (ℎ − ℎ) Differentiating with respect to α, 0 (29)
(30)
= (ℎ − ℎ ) − (ℎ − ℎ) (1 − ℇ⁄ ) (31)
0
= 0 + (32)
From equation 25, we argued that for positive pitch stability 0 > 0. Examining equation 30, it can be seen that for a tailed aircraft, 0 has two parts: first part due to wing and second
part due to fixed incidence of tail. To take aerodynamic advantage, most aircraft use positive camber airfoil which results in negative pitching moment < 0. Therefore overall 0 is then made positive by second term of the equation. So, most designs include horizontal tail to counteract negative pitching moment of wing and provide overall positive moment. Horizontal tails are placed at negative incidence so as to lift down the aircraft at rear end and pitch the nose up.
8.2 Stability for Blended wing body without tail
For Blended wing body aircraft without tail, equation 30 reduces to:
= 0 (33) So, tailless aircraft obviously can't compensate for negative moment. In order to provide longitudinally stability to tailless aircraft, any of the following two designs can be incorporated
[12]:
A) By use of combination of sweep and twist 64
In case of swept back wings, any airfoil can be used by selecting a suitable combination of sweep and twist (Fig 38). Longitudinal stability is provided by combination of sweep and twist. To obtain positive 0 in wing only configuration, the wash out is provided i.e. wings are twisted so that angle of incidence is lower at tips. Negative moment generated by root airfoil is compensated by generating positive moment from wing tips. Due to twist in wing, negative lift is generated at near wing tips which results in overall positive moment coefficient.
Figure 31: Forces acting on swept back wing [36]
B) By use of Reflex Airfoil
By using a reflex camber airfoil and placing the center of gravity front of quarter chord point, static longitudinal stability can be achieved (Fig 32). Reflex camber line produce positive pitching moment and aerodynamic force will act behind the CG. If aircraft nose is pitched up by disturbance, then lift will increase and with L2>L1, it will result in pitch down moment, reducing the angle of attack, until the equilibrium state is reached again. Thus, reflexed airfoil can provide stability to aircraft. Problem with reflex airfoil is that it shifts the lift vs drag polar down, which means lower coefficient of lift at certain angle of attack and also less maximum lift coefficient
[12].
Figure 32: Free body diagram of reflex airfoil [3] 65
8.2.1 Estimation of neutral point
Neutral point is the reference point for which pitching moment does not depend on the angle of attack. Neutral point only depends upon the plane’s external geometry. XFLR 5 software was used to find neutral point. By trial and error, CG was moved backward and polar’s for Cm vs alpha were plotted until straight horizontal curve was obtained, which tells the location of neutral point. For straight horizontal curve XNP=XCG= 73 ft
Figure 33: Cm vs alpha graphs for different CG locations 66
8.2.2 Weight and Balance
Components weight are approximated by using Roskam class I method. For brevity only the main components are considered and there weight’s along with their point mass location is presented in table 21.
Table 21: Point masses and their locations Description Mass Location x (ft) y (ft) z (ft)
Fixed equipment’s 73,315 A 30.000 0.000 0.000
Landing Gear 46,246 B 73.000 0.000 -2.000
Wing 209,237 C 65.926 0.000 1.520
Payload 123,060 D 75.000 0.000 0.000
Fuel 301,170 E 78.000 0.000 2.000
Propulsion system 61,073 F 105.000 0.000 4.000
Figure 34: Point masses Locations
Center of gravity calculations:
The center of gravity locations must be calculated for all feasible loading scenarios. The loading scenarios depend to a large extent on the mission of the airplane. Typical loading combinations applicable to mission designed airplane are:
1. Empty Weight
2. Empty Weight + Fuel 67
3. Empty Weight + Payload n ∑ i=1 mixi 3. Empty Weight + Payload + Fuel (MTOW) Center of gravity can be calculated using equation: CG = n Where M = ∑ i=1 mi
For Empty weight, XCG = 69.714 ft
For empty weight +Payload, XCG = 70.745 ft
For empty Weight + Fuel, XCG = 71.295 FT
For MTOW, XCG =71.79 ft Condition for static stability for BWB:
For Blended Wing Body configuration equation 31 reduces to
= (ℎ − ℎ0) (34)
Or
= − (35)
Where, Kn is called static margin and defined as simply the non-dimensional distance between the aerodynamic center and the CG location.
= ℎ − ℎ = − (36)
0
Kn is positive if CG is ahead of aerodynamic center. The only way to get < 0, if Kn > 0, this means locating the CG ahead of the aerodynamic center of the wing.
For BWB 601, all values of are known for equation 36.
From error and trail approximation, XNP=75 ft.
From XFLR 5, MAC = 56.98 ft.
Using equation 36, CG excursion diagram can be plotted various loading combinations: 68
CG Excursion 10000 diagram 00
80000 MTOW 0 82307 6. 7 ) s 60000 c We+fu c i i b I t t
( 0
a el a t t W s s h 713013 58007 g i e e 40000 e 8 l l b b Empty a W a w t w
0 o o l l l l a a
weight x n i a 20000 M 457018 M 0
0 We+Paylo 0 ad 0.0 0.0 0.0 1 2 0.03 0.04 0.05 0.06 7 0.08 0.09 Static margin,% of MAC
Figure 35: CG excursion diagram
Reference [38] suggests that for tailless aircraft, ultimate static margin is reasonable in range of
0.02 to 0.08. From CG excursion diagram we can see that for various loading combinations, CG lies within this range Thus condition of static stability will be satisfied.
9.0 Dynamic stability and control
9.1 Control surfaces
Control surfaces of tailless aircraft are interesting part of design due to the absence of conventional tail. Tailless aircraft means with or without vertical tail and purely without horizontal tail [35]. The control surfaces for pitch and yaw control for these aircraft are totally different from conventional aircraft. The absence of tail rudder could be substituted by other control surfaces such as split drag flaps, inboard and outboard ailerons, winglets rudders and Thrust Vectoring [35]. The problem of absence of the elevator can solved by substituting it with elevons. The elevons are aircraft control surfaces that serve the functions of both the elevators and the ailerons. They are installed on each side of the aircraft at the trailing edge of the wing. If they elevens on 69 both side are moved in the same direction they will cause a pitching moment (nose up or down).
If moved in opposite direction (one up, one down) they will cause a rolling moment.
For yaw control there are two possible design for BWB aircraft. First one is placing the vertical tail at the tips of wings rather than aft of tail like conventional aircraft. Second one is by using split drag flaps (rudders) as yaw control surfaces.
Split drag flaps consists of upper and lower flaps that will be deflected oppositely. This device works as a drag producer in order to generate yawing moment. Deflection of the flaps on one side of the wing produces asymmetric drag force and, as consequences, yawing moment is produced that rotates the nose of the aircraft toward the deflected flaps. To improve the effectiveness of split flaps they are located near to the wing tips. This provides long moment arm and will give greater yawing moment for the BWB aircraft.
For BWB 601, combination of both wing tip rudder and split drag flaps are proposed considering the reliability and safety issues. Similar configuration was used in Boeing X-48B experimental aircraft and proved to be successful for blended wing body. BWB 601 will have 8 control surfaces, named 1 to 8 as shown in figure 40. For preliminary design, it is assumed that all the flaps or control surfaces have hinge points at x position 80 % chord length and y position
50 % thickness.
Figure 36: BWB 601 control surfaces 70
9.2 Longitudinal, lateral and control derivatives
To get stability and control derivatives BWB-601 was model in XFLR5 and simulation was performed as shown in figure 37.
Figure 37: Modelling of BWB601 in XFLR-5 71
Dimensionless derivatives obtained from XFLR5 simulation are presented in table 22.
Table 22: Dimensionless Aerodynamic stability and control derivatives Longitudinal Derivatives Lateral derivatives Control derivatives
Xu = -1396 Yv = -13817 Xde = -13622
Xw = 7398.5 Yp = -3.0524e+05 Yda = 1.6213e+06 Zu = -36600 Yr = 2.1865e+05 Zde = 3.5829e+06
Zw = -3.6782e+05 Lv = -5.5163e+05 Lda = 1.0527e+08 Zq = -2.9603e+06 Lp = -9.7693e+07 Mde = -3.8566e+07 Mu = -4.6794e-05 Lr = 2.0507e+07 Ndr = -2.7629e+07 Mw = -1.872e+05 Nv = 1.9436e+05 Mq = -1.7281e+07 Np = -9.9659e+05 Nr = -3.8169e+06
State matrices and control matrices obtained are as follows:
Longitudinal state matrix
−0.0038 0.0205 0.000 −9.8100
[ −0.1016 −1.0211 184.875 0.0000 ] (37)
0.000 −0.00111 −1.0299 0. 0000
0 .000 0. 000 1.000 0.000 0
Lateral state matrix
−0.0383 − 0.8474 −192.48 9.8100 0.0000
−0.0426 −7.4474 1.5762 0.0000 0.0000
0.0083 −0.2807 −0.1953 0.0000 0.0000 (38)
0.000 1. 0000 0.0000 0.0000 0.0000
[ 0.000 0.0000 1.0000 0.0000 0.0000 ]
Longitudinal control matrix
−0.03781944
[ −9.947125 ] (39)
−2.298476
0
Lateral control matrix for control surfaces 3 and 4 1.018988 10.12985 [ ] (40) −0.735009
Lateral control matrix for control surfaces 5 and 6 72 −1.019019
−10.13085 [ ] −0.7354143 (41)
Lateral control matrix for control surfaces 7 and 8 −4.501331 −8.126692 [ ] (42) 1.279297
9.3 Dynamic Stability Analysis
The aircraft is said to be dynamically stable if, it eventually returns to equilibrium after being perturbed from initial equilibrium. The difference between Static stability and dynamic stability is that, the static stability deals with the question of how the system will behave in the very short time just after the disturbance, whereas dynamic stability deals with aircraft behavior over long periods of time. In order to conduct dynamic analysis we investigate the motion that occurs after some initial perturbation is applied and from the properties of the motion we can infer or deny stability. It if turns out that the perturbed motion consists of oscillations of increasing amplitude and rapidly increasing departure from the equilibrium state, the aircraft is dynamically unstable; otherwise it is stable. For aircraft dynamic analysis, generally the equations of motion (E.O.M) are developed and then they are solved systematically to observe the time response of various parameters of motion. Space state is one of the convenient ways to describe the EOM and it can be used very effectively in Matlab to observe the time response of aircraft. On the basis of data obtained from XFLR5 both longitudinal and lateral dynamic stability analysis was conducted using Matlab.
9.3.1 Longitudinal Dynamic Stability Analysis
Longitudinal dynamic analysis deals with study of aircraft behavior in longitudinal direction. It includes the parameters: velocity of aircraft along body axis (u), velocity of aircraft 73 perpendicular to body axis (w), pitch rate (q) and pitch angle (Θ). State space representation of equations of motion of BWB601:
−0.0038 0.0205 0.000 −9.8100 −0.0378
−0.1016 −1.0211 184.875 0.0000 −9.9471 [ ] ][ ] + [
[ ] = [ ] (43)
0.000 −0.00111 −1.0299 0. 0000 −2.2984
0 .000 0. 000 1.000 0.000 0 0 Response Transfer functions are obtained by using Matlab and they can be written as:
( ) −0.037819 (s+22.29) (s−16.42) (s+1.585) = (44) ( ) (s^2 + 0.002212s + 0.003569) (s^2 + 2.053s + 3.116)
( ) −9.9471 (s+43.75) (s^2 + 0.003746s + 0.005265) = (45) ( ) (s^2 + 0.002212s + 0.003569) (s^2 + 2.053s + 3.116)
( ) −2.2985 ( +0.9707) ( +0.006054) = (46)
( ) ( ^2 + 0.002212 + 0.003569) ( ^2 + 2.053 + 3.116)
( ) −2.2985 ( +0.9707)( +0.006054) = (47) ( ) ( ^2 + 0.002212 + 0.003569) ( ^2 + 2.053 + 3.116)
It can be observed from all transfer functions that they have a common denominator and this common denominator represents the characteristic equation when equated to zero.
Characteristic equation governs the stability of aircraft and it provides all the important information required for system dynamic stability analysis. Each transfer function has different numerator which governs the magnitude of dynamic stability of each parameter. The characteristics equation for longitudinal dynamics of BWB601 is given by:
∆(s) = ( ^2 + 0.002212 + 0.003569) ( ^2 + 2.053 + 3.116) = 0 (48)
First part of characteristic equation gives a pair of complex roots that describes the phugoid stability mode with following characteristics:
Damping ratio (ζp) = 0.00959
Un-damped natural frequency (ωp) =0.0807 rad/sec 74
Second part of characteristic equation gives a pair of complex roots that describes the short period stability mode with following characteristics:
Damping ratio (ζs) = 0.579
Un-damped natural frequency (ωs) = 1.313 rad/sec
Both the modes, phugoid and short period mode are aerodynamically stable, however their damping ratios are un-acceptably low. To better under the behavior of aircraft we plotted the time response for transfer functions. For analysis we applied 1o degree elevator input both as a tep and impulse and results are plotted by using Matlab. Fig 1 and 2 shows the time response of aircraft for unit step and unit impulse elevator input respectively. .
Figure 37: Time response for unit step of elevator 75
Figure 38: Time response for unit impulse of elevator
From graphs for unit step elevator input: the phugoid oscillations can be observed in all variables, however the magnitude of each stability mode differs in each response variable.
Clearly the stability of responses is same as determined by common denominator but magnitude of each response is different which is determined by the unique numerator of the transfer function. For impulse input both phugoid and short period mode can be observed: phugoid mode is visible in u and Θ variables whereas in w and q short period mode is visible. It can be seen that for phugoid mode u and Θ, oscillations takes long time to die out and for short period modes in q and w variable oscillations dies out rather quickly. 76
9.3.2 Lateral/Directional Static Stability Analysis
Lateral or directional dynamic analysis deals with study of aircraft behavior in lateral direction. It includes the parameters: velocity of aircraft along lateral axis (v), roll rate (p) and yaw rate (r), roll angle (ϕ ) and yaw angle (φ). State space matrices of our given lateral system dynamics as
−0.0383 − 0.8474 −192.48 9.81 0 1.0189 −1.0190 −4.5013
−0.0426 −7.4474 1.5762 0 0 10.1298 −10.1308 −8.1266
= 0.0083 −0.2807 −0.1953 0 0 + −0.7350 0.7354 1.2792 [ ] (49)
∅ 0 1 0 0 0 0 0 0
∅
[ 0 [ ] 0 1 0 0 ] [ ] [ 0 0 0 ]
Using matlab, transfer functions with respect to control surfaces were obtained to investigate lateral dynamics.
Transfer functions with respect to control surfaces 3 and 4:
( ) = 1.019 ( +133.6) ( +4.438) ( +0.01333) (50) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) 10.13 ^2 ( ^2 + 0.1151 + 1.017) = (51) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) −0.73501 ( +3.511) ( +0.5) ( −0.4055) = (52) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
∅( ) 10.13 ( ^2 + 0.1151 + 1.017) = (53) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) −0.73501 ( +3.511) ( +0.5) ( −0.4055) = (54) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
Transfer functions with respect to control surfaces 5 and 6:
( ) −1.019 ( +133.7) ( +4.439) ( +0.01331) = (55) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) −10.131 ^2 ( ^2 + 0.115 + 1.017) = (56) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358) 77
( ) = 0.73541 ( +3.513) ( +0.4997) ( −0.4053) (57) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
∅( ) −10.131 ( ^2 + 0.115 + 1.017) = (58) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) 0.73541 ( +3.513) ( +0.4997) ( −0.4053) = (59) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
Transfer functions with respect to control surfaces 7 and 8:
( ) −4.5013 ( +54.82) ( +5.998) ( −0.002841) = (60) ( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) −8.1267 ^2 ( ^2 − 0.03804 + 0.3168) = (61)
( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) 1.2793 ( +5.661) ( +0.1405) ( −0.1287) = (62)
( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
∅( ) = −8.1267 ( ^2 − 0.03804 + 0.3168) (63)
( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
( ) 1.2793 ( +5.661) ( +0.1405) ( −0.1287) = (64)
( ) ( +7.478) ( −0.004675) ( ^2 + 0.2082 + 1.358)
Similar to longitudinal dynamics we have a common denominator in all transfer functions, which governs the lateral dynamics stability of the A/C, while the numerators are different for each transfer function and they govern the magnitude of each stability response.
Using matlab the time response for impulse input are plotted for all transfer functions as shown in fig 39, 40 and 50. 78
Figure 39: Time response for impulse input of 3 and 4 surfaces
Figure 40: Time response for impulse input of 5 and 6 surfaces 79
Figure 41: Time response for impulse input of 7 and 8 surfaces
It can be seen clearly from above graphs, that after initial disturbance in v, p r, ϕ oscillations eventually will converge and settle down around an equilibrium point. In other words system dynamics are stable in there variables. However for yaw angle (φ) graphs indicates that the system dynamics are marginally stable or neutrally stable.
10.0 BWB 601 Drag estimation.
Drag force is combination of all forces that resist against aircraft motion and is given by following equation.
= 1 2 (65)
2
Where CD is drag coefficient. It is a non-dimensional parameter that takes into account every aerodynamic configuration aspect of the aircraft including wing, tail, fuselage engine, control surfaces, landing gear, rivets and antenna etc.
Total drag is the sum of induced drag (Di) and zero lift drag (Do)
= + (66) 80
Induced drag is the drag directly related to production of lift. In other words it depends upon angle of attack of the aircraft (i.e. lift coefficient). As the angle of attack of the aircraft varies, this type of drag is changed. The induced drag in itself include drag due to vortices and air compressibility. In low subsonic flight, compressibility drag is negligible, but is high subsonic and transonic flight, must be taken into account. In supersonic flight, wave drag is added to the induced drag. The reason is to account for the contribution of shock wave. The induced drag is a function of airspeed, air density, reference area, and the lift coefficient:
= 1 2 (67)
2
Zero lift drag doesn’t have any influence from lift. The zero-lift drag includes all types of drags that do not depend on production of the lift. Every aerodynamic component of aircraft generates zero-lift drag. Typical components are fuselage, wing, tail, landing gear, engine nacelle, strut and antenna. The zero-lift drag is a given by:
1 = 2 (68)
2
In this equation, the coefficient 0 is called zero-lift drag coefficient.
From the equations; one can conclude that drag coefficient has two components:
= + 0 (69) Above equation can be written as (drag polar equation)
= + 2 (70)
0 Where k is the induced drag correction factor and it is inversely proportional to the wing aspect ratio and wing Oswald efficiency factor (e).
1 = =0.051366345 (71)
∏
= + 0.0513 2 (72)
0 81
Procedure for estimation of zero lift drag coefficient
The component built up method was used to estimate zero lift drag coefficient [ ]. According to this technique, drag coefficients of all individual components are added to get total drag coefficient. It takes account of skin friction drag, pressure drag due to viscous separation and interference effects of every component. Miscellaneous drags due to aircraft special features are added to total along with total contribution from leakage and protuberances.
Subsonic zero lift drag according to build up method is given by below equation:
= ∑( ) + + (73)
0 _ &
Where “c” subscript indicates that those values are different for each component. is the flat plate skin friction coefficient, and is a non-dimensional number. For turbulent flow it depends upon
Reynolds number as follow:
0.455 = (74)
2.58 2 0.65 [ ( )] (1+0.144 )
10 Where Re is the Reynolds number.
is the component form factor that estimates pressure drag due to viscous drag separation.
Form factor for subsonic speed is given by:
0. 6 For wing, tail, strut and pylon:= [1 + ( ) + ( ) 4] [1.34 0.18( )0.28] (75)
( )
60 (76)
For fuselage and smooth canopy: = 1 + 3 + 400 0.35
For Nacelle and smooth external surface: = 1 + (77)
Where ( ) is the chord wise location of airfoil maximum thickness point and =
4 = 1 + 2.7 + 100 ( ) ( ) (78) is the maximum thickness to chord ratio of the lifting surface. 82
QC in equation is interference factor. It depends upon mutual interference of components.
10.1 Calculations of zero drag coefficient for center body (Inner wing)
For cruise conditions (Altitude=45000 ft)
Density of air (ρ) = 4.62x10-4 slug/ft3
Dynamic viscosity (μ) =2.969*10-7 lbs. /ft2
Speed of sound (a) =967.5 ft/s
Cruise speed (V=Ma) = 822.4 ft/s
Max thickness to chord ratio (t/c) = 0.12
Reference area is taken as projected area of center body + projected area of outer wing)
Reference area and Swet for center body is evaluated from solid work model (Fig & fig).
2 Reference area= 10054.39 ft .
2 Swet for center body= 2x5626.87 = 13053.74 ft .
Figure 42: Measurement of projected area of center body and outer wing from solid work model 83
Figure 43: Measurement of wet area of Center body from solid work model
Mean aerodynamic chord for center body is calculated by equation:
= 2 [1 + − ] = 85.53 (79)
3 1+
= = 1.09E+08 (80)
0.455 = 1.93E- (81 = _ From equation () 2.58 2 0.65 03 ) [ ( )] (1+0.144 )
10 (82 0.6 4 0.18 From equation () = [1 + ( ) + ( ) ] [1.34 ( )0.28 ] = 1.51E+00 )
( )
Also Qcb=1 (lifting body)
Zero drag coefficient for center = (83 body = _ 0.0038 )
_
10.2 Calculations of zero drag coefficient for outer wing
Swet for outer wing = Total wet area of wing and center body– Wet area of center body
= 2x10470 -13053.74 = 7887 ft^2 84
Figure 44: Measurement of wet area of wing + center body from solid work model
Mean aerodynamic chord for outer wing is calculated by equation:
2 [1 + − ] = 28
= (84)
3 1+
= = 3.57E+07 (85 )
0.455 = 2.26E- = _ 2.58 2 0.65 From equation () [ ( )] (1+0.144 ) 03 10 (86 = ) 0.6 4 1.62E+0 0.18 From equation () = [1 + ( ) + ( ) ] [1.34 ( )0.28 ] 0
( ) (87 ) Also Qow=1 (lifting body) _ Zero drag coefficient for outer wing, _ = = 0.0029
(88 ) 85
10.3 Calculations of zero drag coefficient for Winglets
2 Swet for winglet = 1211.32 ft (from solid work model)
Figure 45: Measurement of Wet area of a winglet from solid work model
Mean aerodynamic chord for outer wing is calculated by equation:
2 [1 + − ] = 16.54
= (89)
3 1+
= = 2.11E+07 (90)
0.455 = From equation () _ = 2.45E-03 (91) 2.58 2 0.65
[ ( )] (1+0.144 )
10 = 0.6 4 1.66E+0 0.18 (92) From equation () = [1 + ( ) + ( ) ] [1.34 ( )0.28 ] 0
( )
Also Qw=1 (lifting body)
Zero drag coefficient for = (93) winglet, = _ 0.0005
_ 86
10.4 Calculations of zero drag coefficient for Nacelle
Swet for Nacelle = 4x347.641390.56 ft^2 (from solid work model)
Figure 46: Measurement of Wet area of a winglet from solid work model
Length of Nacelle (Ln) = 15ft = = 1.91E+07
0.455 = 2.49E- = _
From equation () 2.58 2 0.65 03
[ ( )] (1+0.144 ) 10 (94) = 0.35 From equation () = 1 + 1.18E+00 (95)
From reference interference factor between nacelle and center body, Qw=1.3 _ Zero drag coefficient for Nacelle, _ = = 0.0005 (96)
10.5 Total zero lift coefficient
Total drag coefficient was obtained from summation of drag coefficients of all components and adding miscellaneous and leakage & protuberance drag. Assuming, = 10% of = 4% of _ 0 & 0 87
= ∑( ) + + (97)
0 _ &
0 = 0.0077 + 0.10 + 0.04 (98)
0 = 0.009
10.6 Drag polar
From equation 1 and 2 we get
= 0.009 + 0.0513 2 (99)
Drag polar for BWB-601 is presented in figure
Drag polar for BWB 601 for cruise conditions 0.8
0.7
0.6 l C
t 0.5 f i l
f
o 0.4
t n e i 0.3 c ffi
e 0.2 o C 0.1
0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Coefficent of Drad Cd
Figure : Drag polar for BWB 601 88
10.0 Conclusions or Discussions
To meet the goals of green aviation: fuel efficiency, emissions and noise, there is a definite need of new solutions. Although, there are number of alternatives including engine modifications, alternative fuels, and changing accent & decent approach but nothing seems as promising as BWB aircraft. Preliminary sizing of BWB 601 shows the weight saving of 19.8 percent in comparison to Boeing 747-8I for almost same payload. Placing of engine over the center body offered the noise shielding from ground. The advances in flight and control technology have made it possible to fly BWB as safer as like that of conventional configuration.
Dynamic stability and control analysis has proven that BWB601 is controllable and safe to fly.
In future work, CFD analysis can be done using real CFD software’s like Ansys Fluent to predict the aerodynamic gains of BWW601 configuration. 89
References
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Appendices
Appendix A: Matlab code for longitudinal dynamics
% Matlab code for longitudinal dynmics stability of BWB601 clc; % Defining State Matrix A =[-0.00387572 0.0205402 0 -9.81 -0.101611 -1.02117 184.876 0 0 -0.0111568 -1.02993 0 0 0 1 0 ] % Defing input matrix B =[-0.03781944 -9.947125 -2.298476 0 ] C = eye(4); % C matrix is identity matrix 4x4 D = zeros(length(C),1); % D Matrix is zero matrix 4x1 sys = ss(A,B,C,D); TF = tf(sys); % This will gives us 4 transfer functions % Obtaining tranfer functions and defining each % tranfer function with clear name and label setting [num,den]=ss2tf(A,B,C,D); disp('TF from n --> u') disp('------') TF_n2u = zpk(tf(num(1,:),den)) disp('TF from n --> w') disp('------') TF_n2w = zpk(tf(num(2,:),den)) disp('TF from n --> q') disp('------') TF_n2q = zpk(tf(num(3,:),den)) disp('TF from n --> theta') disp('------') TF_n2th = zpk(tf(num(4,:),den))
% Plots for step input figure, subplot(4,1,1),step(TF_n2u*pi/180,'-g'),ylabel('u[ft/sec]') title('Response to step input of \eta ') subplot(4,1,2),step(TF_n2w*pi/180,'-g'),ylabel('w[ft/sec]') title('Response to step input of \eta ') subplot(4,1,3),step(TF_n2q*pi/180,'-g'),ylabel('q[rad/sec]') title('Response to step input of \eta ') subplot(4,1,4),step(TF_n2th*pi/180,'-g'),ylabel('\theta[rad]') title('Response to step input of \eta ') % Plots for impulse input figure, 94 subplot(4,1,1),impulse(TF_n2u*pi/180,'-g'),ylabel('u[ft/sec]') title('Response to impulse input of \eta ') subplot(4,1,2),impulse(TF_n2w*pi/180,'-g'),ylabel('w[ft/sec]') title('Response to impulse input of \eta ') subplot(4,1,3),impulse(TF_n2q*pi/180,'-g'),ylabel('q[rad/sec]') title('Response to impulse input of \eta ') subplot(4,1,4),impulse(TF_n2th*pi/180,'-g'),ylabel('\theta[rad]') title('Response to impulse input of \eta ')
% Eigenvalues of Long. system dynamics eig(A) % Eigenvalues and Eigenvector analysis [EigVec,EigVal] = eig(A); for ii = 1:length(A) disp(['Eigenvector associated with the ',num2str(ii),' eigenvalue']) disp('------') EigVal(ii,ii),EigVec(:,ii), end
%% % Another important analysis could be conducted by investigating the % eigenvectors and their amplitude to see the individual effect of each % mode on state dynamics. Mag_of_EigVec = [abs(EigVec(:,1)) abs(EigVec(:,2)) ... abs(EigVec(:,3)) abs(EigVec(:,4))]; damp(A) disp(' Short Period Mode | Phugoid Mode') disp(' ------') disp(['u | ',num2str(Mag_of_EigVec(1,1:2)),' | ',num2str(Mag_of_EigVec(1,3:4))]) disp(['w | ',num2str(Mag_of_EigVec(2,1:2)),' | ',num2str(Mag_of_EigVec(2,3:4))]) disp(['q | ',num2str(Mag_of_EigVec(3,1:2)),' | ',num2str(Mag_of_EigVec(3,3:4))]) disp(['theta | ',num2str(Mag_of_EigVec(4,1:2)),' | ',num2str(Mag_of_EigVec(4,3:4))])
% Damping ratio: damp(A) 95
Appendix B: Matlab code for Lateral dynamics
% Matlab code for lateral or directional dynamics anlysis % First, we will construct the state space matrices of our given lateral % system dynamics as clc clear all A=[ -0.0383595 -0.847425 -192.488 9.81 0 -0.0426963 -7.44743 1.57629 0 0 0.0083637 0.280703 -0.195392 0 0 0 1 0 0 0 0 0 1 0 0]
B= [ 1.018988 -1.019019 -4.501331 10.12985 -10.13085 -8.126692 -0.7350099 0.7354143 1. 279297 0 0 0 0 0 0 ];
C = eye(length(A));
D = [ 0 0 0; 0 0 0 ; 0 0 0; 0 0 0; 0 0 0];
% Transfer Functions for ailrons or flaps 3 amd 4:
[num1,den1] = ss2tf(A,B,C,D,1); disp('TF from ksi(ail) --> v') disp('------') TF_ksi2v = zpk(tf(num1(1,:),den1)) disp('TF from ksi(ail) --> p') disp('------') TF_ksi2p = zpk(tf(num1(2,:),den1)) disp('TF from ksi(ail) --> r') disp('------') TF_ksi2r = zpk(tf(num1(3,:),den1)) disp('TF from ksi(ail) --> phi') disp('------') TF_ksi2phi = zpk(tf(num1(4,:),den1)) disp('TF from ksi(ail) --> psi') disp('------') TF_ksi2psi = zpk(tf(num1(5,:),den1))
% Transfer Functions for flaps 5 amd 6:
[num2,den2] = ss2tf(A,B,C,D,2); 96
disp('TF from zeta(rudder_flap) --> v') disp('------') TF_zeta2v = zpk(tf(num2(1,:),den2)) disp('TF from zeta(rudder_flap) --> p') disp('------') TF_zeta2p = zpk(tf(num2(2,:),den2)) disp('TF from zeta(rudder_flap) --> r') disp('------') TF_zeta2r = zpk(tf(num2(3,:),den2)) disp('TF from zeta(rudder_flap) --> phi') disp('------') TF_zeta2phi = zpk(tf(num2(4,:),den2)) disp('TF from zeta(rudder_flap) --> psi') disp('------') TF_zeta2psi = zpk(tf(num2(5,:),den2)) % Transfer Functions for rudder flaps 7 amd 8: [num3,den3] = ss2tf(A,B,C,D,3); disp('TF from zeta(rud) --> v') disp('------') TF_zeta2v = zpk(tf(num3(1,:),den3)) disp('TF from zeta(rud) --> p') disp('------') TF_zeta2p = zpk(tf(num3(2,:),den3)) disp('TF from zeta(rud) --> r') disp('------') TF_zeta2r = zpk(tf(num3(3,:),den3)) disp('TF from zeta(rud) --> phi') disp('------') TF_zeta2phi = zpk(tf(num3(4,:),den3)) disp('TF from zeta(rud) --> psi') disp('------') TF_zeta2psi = zpk(tf(num3(5,:),den3))
%% m=eig(A);
% Eigenvalues and Eigenvector analysis [EigVec,EigVal] = eig(A); for ii = 1:length(A) disp(['Eigenvector associated with the ',num2str(ii),' eigenvalue']) disp('------') EigVal(ii,ii),EigVec(:,ii), end 97
% Damping ratio, natural frequency of modes damp(A)
% Solutions of given Lat. EoMs t = [0:1e-2:SimTime]; % simulation time vector u = zeros(length(t),1); % input vector
% Create the step input in matlab indx_t_1 = find(t == 1); % we need to specifiy when the step input will ramp up indx_ t_2 = find(t == 2); % we need to specify when the step input will die down %indx_t_ 3 = find(t == 50); % we need to specifiy when the step input will ramp up %indx _t_4 = find(t == 51); % we need to specify when the step input will die down %indx_t_ 5 = find(t == 75); % we need to specifiy when the step input will ramp up %indx_t_6 = find(t == 76); u_imp_ail = u; % create impulse input for only aileron active u_imp_rud = u; % create impulse input for only rudder active u_imp_flap =u;
% Plotting response for control surfaces 3 and 4 for unit impulse input % And then the next thing is to simulate the results as the following: u_imp_ail(indx_t_1:indx_t_2,1) = 1*pi/180; % construct impulse input in [RAD] u_imp_rud(indx_t_1:indx_t_2,1) = 0*pi/180; % construct impulse input in [RAD] u_imp_flap(indx_t_1:indx_t_2,1) = 0*pi/180; lat_sys = ss(A,B,C,D); [y_lsim, t_lsim] = lsim(lat_sys,[u_imp _ail u_imp_rud u_imp_flap],t); % store all outputs for further investigation figure, subplot(5,1,1) plot(t_lsim,y_lsim(:,1),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('v[ft/sec]') title('Response to control surfaces 3,4 for impulse input') subplot(5,1,2) plot(t_lsim,y_lsim(:,2),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('p[rad/sec]') subplot(5,1,3) plot(t_lsim,y_lsim(:,3),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('r[rad/sec]') subplot(5,1,4) plot(t_lsim,y_lsim(:,4),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('\phi[rad]') subplot(5,1,5) plot(t_lsim,y_lsim(:,5),'- g', 'LineWidth',2),xlabel('Time(sec)'),ylabel('\psi[rad]') %% % Plotting response for control surfaces 5 and 6 for unit impulse input % And then the next thing is to simulate the results as the following: u_imp_ail(indx_t_1:indx_t_2,1) = 0*pi/180; % construct impulse input in [RAD] 98 u_imp_rud(indx_t_1:indx_t_2,1) = 1*pi/180; % construct impulse input in [RAD] u_imp_flap(indx_t_1:indx_t_2,1) = 0*pi/180; lat_sys = ss(A,B,C,D);
[y_lsim, t_lsim] = lsim(lat_sys,[u_imp _ail u_imp_rud u_imp_flap],t); % store all outputs for further investigation figure, subplot(5,1,1) plot(t_lsim,y_lsim(:,1),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('v[ft/sec]') title('Response to control surfaces 5,6 for impulse input') subplot(5,1,2) plot(t_lsim,y_lsim(:,2),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('p[rad/sec]') subplot(5,1,3) plot(t_lsim,y_lsim(:,3),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('r[rad/sec]') subplot(5,1,4) g','LineWidth',2),xlabel('Time(sec)'),ylabel('\phi[rad]') subplot(5,1,5) plot(t_lsim,y_lsim(:,4),'- plot(t_lsim,y_lsim(:,5),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('\psi[rad]') % Plotting response for control surfaces 7 and 8 for unit impulse input % And then the next thing is to simulate the results as the following: u_imp_ail(indx_t_1:indx_t_2,1) = 0*pi/180; % construct impulse input in [RAD] u_imp_rud(indx_t_1:indx_t_2,1) = 0*pi/180; % construct impulse input in [RAD] u_imp_flap(indx_t_1:indx_t_2,1) = 1*pi/180; lat_sys = ss(A,B,C,D); [y_lsim, t_lsim] = lsim(lat_sys,[u_imp _ail u_imp_rud u_imp_flap],t); % store all outputs for further investigation figure, subplot(5,1,1) plot(t_lsim,y_lsim(:,1),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('v[ft/sec]') title('Response to control surfaces 7 and 8 for impulse input') subplot(5,1,2) plot(t_lsim,y_lsim(:,2),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('p[rad/sec]') subplot(5,1,3) plot(t_lsim,y_lsim(:,3),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('r[rad/sec]') subplot(5,1,4) plot(t_lsim,y_lsim(:,4),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('\phi[rad]') subplot(5,1,5) plot(t_lsim,y_lsim(:,5),'- g','LineWidth',2),xlabel('Time(sec)'),ylabel('\psi[rad]')